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Year 7 · Key Stage 3 · free KS3 maths worksheet

Algebraic notation

12 original questions, 32 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Simplify  a + a + a + a

1 mark
Show answer
4a
2

Write each of these in its simplest algebraic form.

  1. b × 5 × a
  2. y + y + y
  3. m × m × n
  4. p ÷ 4
4 marks
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a) 5ab b) 3y c) m2n d) p/4
3

Simplify  d × d × d

1 mark
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d3
4

Look at 53

  1. Write down the base.
  2. Write down the index (also called the power or exponent).
  3. Write 7 × 7 × 7 × 7 using index notation.
3 marks
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a) 5 b) 3 c) 74
5

Write down whether each of these is an expression, an equation or a formula.

  1. 3x + 2
  2. 2y − 5 = 11
  3. A = lw
  4. 4a + b2
2 marks
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a) expression b) equation c) formula d) expression
6

Pencils cost c pence each.

Write down an expression, in terms of c, for the total cost, in pence, of 7 pencils.

1 mark
Show answer
7c
7

Amy is x years old.

Ben is 5 years older than Amy.

Chloe is twice as old as Amy.

  1. Write down an expression, in terms of x, for Ben's age.
  2. Write down an expression, in terms of x, for Chloe's age.
2 marks
Show answer
a) x + 5 (accept 5 + x) b) 2x
8

Write an expression for each of these.

  1. Square n, then add 4
  2. Add 4 to n, then square the answer
  3. Cube t, then halve the answer
  4. Multiply p by q, then divide by 3
4 marks
Show answer
a) n2 + 4 b) (n + 4)2 c) t3/2 d) pq/3
9

A plumber charges a fixed call-out fee of £40 plus £28 for each hour of work.

The plumber works for h hours on a job.

The total charge for the job is £C.

Write a formula for C in terms of h.

3 marks
Show answer
C = 40 + 28h
10

Asha thinks of a number, n.

She multiplies her number by 4 and then subtracts 7. Her answer is 25.

  1. Write an equation in n.
  2. Solve your equation to find Asha's number.
3 marks
Show answer
a) 4n - 7 = 25 b) n = 8
11

A square tile has sides of length s cm.

  1. Write a formula for the area, A cm2, of one tile.
  2. Six tiles are put in a row, as shown in the diagram. Write a formula for the perimeter, P cm, of the row of tiles.
  3. Rearrange your answer to part (a) to write a formula for s in terms of A.
sDiagram NOT accurately drawn
4 marks
Show answer
a) A = s2 b) P = 14s c) s = √A
12

A rectangle has length (x + 6) cm and width x cm.

The perimeter of the rectangle is 40 cm.

  1. Write an equation in x. Simplify your equation.
  2. Solve your equation to find the length of the rectangle.
4 marks
Show answer
a) 4x + 12 = 40 b) 13 cm

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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